Health-aware optimal charging of lithium-ion batteries using deep-neural networks-based explicit constrained model predictive control

The use of Model Predictive Control (MPC) for optimal charging of batteries is attracting attention due to its superiority over empirical charging protocols. But, the intricate nature of physics-based battery models poses a challenge to MPC implementation, necessitating substantial computational resources. Hence, this paper presents a method for explicit MPC based on machine learning (ML) models, applied for optimal battery charging while accounting for linear health constraints. The method uses Deep Neural Networks (DNNs) to construct offline control law that precisely describe the optimal charging current as a function of the battery's state. This DNN-based control law is developed using data generated by solving the MPC problem several times while varying the battery's initial state. Then, the control law is applied online to regulate the charging by cheaply predicting the closed-loop current. The method is numerically validated by its application to two case studies, showing: i) high accuracy in predicting closed-loop charging current (a normalized root mean square error of less than 1.0 %), ii) robustness in handling random initial states of the battery, iii) capability to learn bound and linear constraints directly from the data without any knowledge of their mathematical formulations, achieving a maximum constraint violation of an order of magnitude equal to 10^-2, iv) applicability to distinct types of battery models, and v) a reduction in the required computational time compared to traditional MPC, which reaches up to 94.7%, in the lowest-performing testing scenario.